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Theorem ordtr1 4074
Description: Transitive law for ordinal classes. (Contributed by NM, 12-Dec-2004.)
Assertion
Ref Expression
ordtr1 (Ord 𝐶 → ((A B B 𝐶) → A 𝐶))

Proof of Theorem ordtr1
StepHypRef Expression
1 ordtr 4064 . 2 (Ord 𝐶 → Tr 𝐶)
2 trel 3835 . 2 (Tr 𝐶 → ((A B B 𝐶) → A 𝐶))
31, 2syl 14 1 (Ord 𝐶 → ((A B B 𝐶) → A 𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1374  Tr wtr 3828  Ord word 4048
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-in 2901  df-ss 2908  df-uni 3555  df-tr 3829  df-iord 4052
This theorem is referenced by:  ontr1  4075  dfsmo2  5824  smores2  5831  smoel  5837
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